The generator matrix

 1  1  1  1  1  1  1  1  X  0  X X^3+X^2  1  1
 0  X X^3+X^2 X^2+X X^3 X^3+X^2+X X^2 X^3+X X^2+X  X X^3+X  X  0 X^3+X^2

generates a code of length 14 over Z2[X]/(X^4) who´s minimum homogenous weight is 13.

Homogenous weight enumerator: w(x)=1x^0+40x^13+44x^14+40x^15+1x^16+2x^20

The gray image is a linear code over GF(2) with n=112, k=7 and d=52.
This code was found by Heurico 1.16 in 3.81e-009 seconds.